# UNC MATH 231 Calculus I: Syllabus, Topics and Practice

> A study guide for UNC Chapel Hill MATH 231, Calculus of Functions of One Variable I: limits, derivatives and integrals, with practice.

Source: https://practicecalculus.com/courses/unc-chapel-hill-math-231
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 231
- **Credits:** 4
- **Prerequisites:** MATH 110 and 130, with a C- or better in MATH 130, or placement by the department
- **Covers:** Limits, derivatives and integrals of functions of one variable
- **Gen Ed:** IDEAs in Action FC-QUANT (FY-LAUNCH in designated sections)
- **Support course:** MATH 231L Calculus I Corequisite (1 credit, pass/fail)
- **Next course:** MATH 232 Calculus of Functions of One Variable II
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 231 is the 4-credit Calculus I course at UNC Chapel Hill, covering limits, derivatives and integrals of functions of one variable.
- You need MATH 110 and 130 with a C- or better in MATH 130, or placement by the department.
- MATH 231L is an optional 1-credit pass/fail corequisite that reviews algebra and trigonometry just in time.
- A C- or better in MATH 231 is the prerequisite for MATH 232.

**UNC MATH 231** (Calculus of Functions of One Variable I) is the first course in the University of North Carolina at Chapel Hill calculus sequence: MATH 231, MATH 232, then MATH 233. It carries 4 credits and meets the IDEAs in Action FC-QUANT requirement. This guide turns the official description into a topic map with lessons you can practice right away.

## What UNC MATH 231 covers

The UNC mathematics department lists MATH 231 with a short description: limits, derivatives, and integrals of functions of one variable. An honors version is available. The listing does not give a week-by-week schedule or textbook, so those come from your instructor.

Those three words cover a standard **Calculus 1** course. In practice that means computing limits and checking continuity, building the derivative from a limit, learning the rules for differentiating polynomial, trig, exponential and log functions, applying derivatives to rates and optimization, and finishing with antiderivatives, definite integrals and the Fundamental Theorem of Calculus. The map below follows that order.

## MATH 231 topic map

| MATH 231 topic | Practice | Read |
| --- | --- | --- |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| One-sided and infinite limits | [One-sided and infinite limits](/learn/calculus-1/limits/one-sided-and-infinite-limits) | [Limits at infinity](/blog/limits-at-infinity) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| The derivative | [Limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivative rules | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Product and quotient rules](/blog/product-and-quotient-rules) |
| Chain rule | [Chain rule in general](/learn/calculus-1/derivative-rules/chain-rule-general) | [Chain rule](/blog/chain-rule) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation](/blog/implicit-differentiation) |
| Applications of derivatives | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Related rates](/blog/related-rates) |
| Mean Value Theorem | [Linear approximation and the MVT](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean Value Theorem](/theorems/mean-value-theorem) |
| Antiderivatives | [Reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums](/blog/riemann-sums) |
| Fundamental Theorem | [Fundamental Theorem, part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem](/blog/fundamental-theorem-of-calculus) |

## MATH 231 and the other UNC calculus options

| Course | Credits | Who it suits |
| --- | --- | --- |
| MATH 152 Calculus for Business and Social Sciences | 3 | Business and social science students; terminal, not preparation for MATH 232 |
| MATH 231 Calculus of Functions of One Variable I | 4 | Students starting the full calculus sequence |
| MATH 231L Calculus I Corequisite | 1 | MATH 231 students who want algebra and trig review |

After MATH 231 come [MATH 232](/courses/unc-chapel-hill-math-232) and [MATH 233](/courses/unc-chapel-hill-math-233).

## Example problems at the MATH 231 level

**1. A limit at infinity.**

$$\lim_{x \to \infty} \frac{5x^2 - x}{2x^2 + 7} = \frac{5}{2}$$

**2. A chain rule derivative.**

$$\frac{d}{dx}\sin(x^3) = 3x^2 \cos(x^3)$$

**3. A definite integral.**

$$\int_0^{\pi} \sin x\,dx = \left[-\cos x\right]_0^{\pi} = 1 + 1 = 2$$

## How to do well in MATH 231

- **Fix precalculus gaps in week one.** If trig or logs feel shaky, consider MATH 231L, and run through the [functions warm-up](/learn/calculus-1/functions-warmup/key-trig-values).
- **Aim well above a C-.** MATH 232 needs a C- or better in MATH 231, and the material builds directly on it.
- **Practice derivative rules in mixed sets** so you learn to recognize which rule applies. Try [derivative rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice).
- **Write out every step in word problems:** a picture, the variables, the equation, then the calculus.
- **Use the [formula sheet](/formulas)** and timed [practice exams](/practice) before midterms.

> **Tip:** in optimization, check the endpoints of the interval as well as the critical points. The largest value is often at an endpoint.

## Frequently asked questions

### What is MATH 231 at UNC?

MATH 231 Calculus of Functions of One Variable I is UNC Chapel Hill's first-semester calculus course. The department describes it as limits, derivatives, and integrals of functions of one variable. An honors version is available.

### What is the prerequisite for MATH 231?

MATH 110 and 130, with a grade of C- or better in MATH 130, or placement by the department.

### What is MATH 231L?

MATH 231L Calculus I Corequisite is a 1-credit pass/fail course taken alongside MATH 231. It gives just-in-time review of algebra and trigonometry and extra practice on the harder Calculus 1 topics.

### Can I take MATH 231 after MATH 152?

You cannot receive credit for MATH 231 after receiving credit for MATH 152 Calculus for Business and Social Sciences. MATH 152 is a terminal course and is not preparation for MATH 232.

### What comes after MATH 231?

MATH 232 Calculus of Functions of One Variable II, which requires a C- or better in MATH 231 or placement by the department.